Answer:
a = 7
Step-by-step explanation:
Using the Cosine rule in the triangle
a² = b² + c² - (2bc cosA )
= 2² + (5[tex]\sqrt{3}[/tex] )² - (2 × 2 × 5[tex]\sqrt{3}[/tex] × cos30° )
= 4 + 75 - (20[tex]\sqrt{3}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) ← exact value of cos30°
= 79 - ( 10 × 3)
= 79 - 30
= 49 ( take square root of both sides )
a = [tex]\sqrt{49}[/tex] = 7
